Finite Group Databasebeta

← C11×#22770 #14599963

Subgroups — C11×#22770 #14599963

Order 2816.

914 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C11×SD16C211yesmaximal, characteristic
2C11×#2355C211yesmaximal, characteristic, complemented
3D4×C11×C4⋊C4C211yesmaximal, characteristic
4C11×#1933C212yesmaximal, complemented
5C11×#1919C212yesmaximal, complemented
6C11×#1877C212yesmaximal
7C11×#1834C211yesmaximal, characteristic, complemented
8C11×#1803C211yesmaximal, characteristic, complemented
9C11×#1802C211yesmaximal, characteristic
10C8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
11C4×C11×#102C212yesmaximal
12C22×C11×SD16C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2212yes—
15C2×C4×D4×C11C2211yescharacteristic
16C22×C11×C4⋊C4—21no—
17C4×C11×SD16C418yescomplemented
18C2×C11×#106C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#103C2212yes—
21C2×C11×#103C2211yescharacteristic
22C2×C11×#102C2212yes—
23C2×C11×#102C2211yescharacteristic
24C2×C4×C8×C11C2212yes—
25C2×C4×C8×C11C2211yescharacteristic
26C11×#391C2212yes—
27C11×#389C2212yes—
28C11×#387—22no—
29C11×#385—22no—
30C11×#384C2211yescharacteristic
31C11×#384C2211yescharacteristic
32C11×#382—21no—
33C11×#380—21no—
34C4×C11×C4⋊C4—21no—
35C4×C11×C4⋊C4C2212yes—
36C4×C11×C4⋊C4C2211yescharacteristic
37C11×#340C2212yes—
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#336C2212yes—
42C22×Q8×C11C2311yescharacteristic
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C23×C4×C11—22no—
46C2×C11×SD16—22no—
47C2×C11×SD16—22no—
48C2×C11×SD16C2×C414yes—
49C22×C8×C11C2312yes—
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C4×Q8×C11—22no—
53C4×Q8×C11C2×C414yescomplemented
54C4×D4×C11—24no—
55C4×D4×C11—22no—
56C4×D4×C11—42no—
57C4×D4×C11C2×C414yes—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—44no—
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—22no—
73C2×C42×C11—21no—
74C2×C42×C11—22no—
75C2×C42×C11C2312yes—
76C2×C42×C11C2311yescharacteristic
77C11×#106C2×C414yescomplemented
78C11×C4⋊C8—22no—
79C11×#103—42no—
80C11×#103C2×C414yescomplemented
81C11×#102—24no—
82C11×#102C2×C414yes—
83C4×C8×C11—42no—
84C4×C8×C11C2×C414yescomplemented
85C11×#95—22no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95D412yes—
90#22770C1111yesmaximal, characteristic, direct product factor, Sylow
91C24×C11—21no—
92C2×Q8×C11—21no—
93C2×Q8×C11—21no—
94C2×Q8×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11C22×C412yes—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11C22×C412yes—
102C2×D4×C11#4112yes—
103C2×D4×C11#4112yes—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—24no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—44no—
111C22×C4×C11—42no—
112C22×C4×C11—42no—
113C22×C4×C11—44no—
114C22×C4×C11—82no—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2411yescharacteristic
120C11×SD16—28no—
121C2×C8×C11—21no—
122C2×C8×C11—21no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—21no—
126C2×C8×C11—22no—
127C2×C8×C11—21no—
128C2×C8×C11C22×C412yes—
129C2×C8×C11C22×C412yes—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—44no—
139C11×C4⋊C4—42no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4—81no—
142C11×C4⋊C4—81no—
143C11×C4⋊C4SD1614yescomplemented
144C11×C4⋊C4C22×C412yes—
145C11×C4⋊C4C22×C412yes—
146C11×C22⋊C4—24no—
147C11×C22⋊C4—44no—
148C42×C11—24no—
149C42×C11—22no—
150C42×C11—22no—
151C42×C11—82no—
152C42×C11C22×C412yes—
153C42×C11#4112yes—
154C2×C4×SD16C2×C1111yescharacteristic
155#2355C2×C1111yescharacteristic, complemented
156D4×C4⋊C4C2×C1111yescharacteristic
157#1933C2×C1112yescomplemented
158#1919C2×C1112yescomplemented
159#1877C2×C1112yes—
160#1834C2×C1111yescharacteristic, complemented
161#1803C2×C1111yescharacteristic, complemented
162#1802C2×C1111yescharacteristic
163C8×C4⋊C4C2×C1111yescharacteristic, complemented
164C4×#102C2×C1112yes—
165C23×C11—22no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—41no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11C22×D411yescharacteristic
173Q8×C11—22no—
174Q8×C11—22no—
175Q8×C11—41no—
176Q8×C11—41no—
177D4×C11—22no—
178D4×C11—22no—
179D4×C11—22no—
180D4×C11#11714yes—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—48no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—88no—
205C2×C4×C11C4×D412yes—
206C2×C4×C11C4×D412yes—
207C2×C4×C11C2×SD1614yes—
208C2×C4×C11C2×SD1612yes—
209C2×C4×C11#13512yes—
210C2×C4×C11C23×C411yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C2×C4×C11H(5,𝔽2)11yescharacteristic
215C2×C4×C112−1+411yescharacteristic
216C8×C11—22no—
217C8×C11—22no—
218C8×C11—42no—
219C22×SD16C22×C1111yescharacteristic
220C2×C4×Q8C22×C1111yescharacteristic
221C2×C4×D4C22×C1112yes—
222C2×C4×D4C22×C1111yescharacteristic
223C22×C4⋊C4—21no—
224C4×SD16C4×C1118yescomplemented
225C2×#106C22×C1111yescharacteristic
226C2×C4⋊C8C22×C1111yescharacteristic
227C2×#103C22×C1112yes—
228C2×#103C22×C1111yescharacteristic
229C2×#102C22×C1112yes—
230C2×#102C22×C1111yescharacteristic
231C2×C4×C8C22×C1112yes—
232C2×C4×C8C22×C1111yescharacteristic
233#391C22×C1112yes—
234#389C22×C1112yes—
235#387—22no—
236#385—22no—
237#384C22×C1111yescharacteristic
238#384C22×C1111yescharacteristic
239#382—21no—
240#380—21no—
241C4×C4⋊C4—21no—
242C4×C4⋊C4C22×C1112yes—
243C4×C4⋊C4C22×C1111yescharacteristic
244#340C22×C1112yes—
245#340C22×C1112yes—
246#340C22×C1112yes—
247#340C22×C1112yes—
248#336C22×C1112yes—
249C22×C11—24no—
250C22×C11—42no—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11—42no—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11C2×C4×D411yescharacteristic
257C22×C11#54611yescharacteristic
258C22×C11#54811yescharacteristic
259C22×C11C22×SD1611yescharacteristic
260C22×C11C2×#13511yescharacteristic
261C22×C11#57611yescharacteristic
262C22×C11#57811yescharacteristic
263C4×C11—22no—
264C4×C11—24no—
265C4×C11—42no—
266C4×C11—42no—
267C4×C11—42no—
268C4×C11—42no—
269C4×C11—82no—
270C4×C11—82no—
271C4×C11C4×SD1614yes—
272C4×C11C2×#11711yescharacteristic
273C4×C11#52011yescharacteristic
274C4×C11#55211yescharacteristic
275C4×C11#55311yescharacteristic
276C22×Q8C23×C1111yescharacteristic
277C22×D4C23×C1111yescharacteristic
278C23×C4—21no—
279C23×C4—22no—
280C2×SD16—22no—
281C2×SD16—22no—
282C2×SD16C2×C4×C1114yes—
283C22×C8C23×C1112yes—
284C22×C8C23×C1111yescharacteristic
285C22×C8C23×C1111yescharacteristic
286C4×Q8—22no—
287C4×Q8C2×C4×C1114yescomplemented
288C4×D4—24no—
289C4×D4—22no—
290C4×D4—42no—
291C4×D4C2×C4×C1114yes—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4D4×C1111yescharacteristic
300C2×C4⋊C4D4×C1111yescharacteristic
301C2×C4⋊C4C23×C1112yes—
302C2×C4⋊C4C23×C1112yes—
303C2×C4⋊C4C23×C1111yescharacteristic
304C2×C4⋊C4C23×C1111yescharacteristic
305C2×C22⋊C4—21no—
306C2×C22⋊C4—22no—
307C2×C42—21no—
308C2×C42—22no—
309C2×C42C23×C1112yes—
310C2×C42C23×C1111yescharacteristic
311#106C2×C4×C1114yescomplemented
312C4⋊C8—22no—
313#103—42no—
314#103C2×C4×C1114yescomplemented
315#102—24no—
316#102C2×C4×C1114yes—
317C4×C8—42no—
318C4×C8C2×C4×C1114yescomplemented
319#95—22no—
320#95—22no—
321#95—22no—
322#95—22no—
323#95D4×C1112yes—
324C2×C11—44no—
325C2×C11#235211yescharacteristic
326C2×C11C2×C4×SD1611yescharacteristic
327C2×C11#295111yescharacteristic
328C2×C11#329511yescharacteristic
329C2×C11#330211yescharacteristic
330C2×C11#335911yescharacteristic
331C2×C11#336111yescharacteristic
332C24—21no—
333C2×Q8—21no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8C22×C4×C1112yes—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4C22×C4×C1112yes—
343C2×D4C11×#4112yes—
344C2×D4C11×#4112yes—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—24no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—44no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—44no—
355C22×C4—82no—
356C22×C4C2×D4×C1112yes—
357C22×C4C2×D4×C1111yescharacteristic
358C22×C4C2×D4×C1112yes—
359C22×C4C2×D4×C1111yescharacteristic
360C22×C4C24×C1111yescharacteristic
361SD16—28no—
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8—22no—
367C2×C8—22no—
368C2×C8—22no—
369C2×C8C22×C4×C1112yes—
370C2×C8C22×C4×C1112yes—
371C4⋊C4—24no—
372C4⋊C4—22no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—44no—
380C4⋊C4—42no—
381C4⋊C4—42no—
382C4⋊C4—81no—
383C4⋊C4—81no—
384C4⋊C4C11×SD1614yescomplemented
385C4⋊C4C22×C4×C1112yes—
386C4⋊C4C22×C4×C1112yes—
387C22⋊C4—24no—
388C22⋊C4—44no—
389C42—24no—
390C42—22no—
391C42—22no—
392C42—82no—
393C42C22×C4×C1112yes—
394C42C11×#4112yes—
395C11#2277011yescharacteristic, direct product factor, Sylow
396C23—22no—
397C23—22no—
398C23—22no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23C22×D4×C1111yescharacteristic
404Q8—22no—
405Q8—22no—
406Q8—41no—
407Q8—41no—
408D4—22no—
409D4—22no—
410D4—22no—
411D4C11×#11714yes—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—48no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—88no—
436C2×C4C4×D4×C1112yes—
437C2×C4C4×D4×C1112yes—
438C2×C4C2×C11×SD1614yes—
439C2×C4C2×C11×SD1612yes—
440C2×C4C11×#13512yes—
441C2×C4C23×C4×C1111yescharacteristic
442C2×C4C2×C11×#4111yescharacteristic
443C2×C4C2×C11×#4111yescharacteristic
444C2×C4C2×C11×#4111yescharacteristic
445C2×C4C11×H(5,𝔽2)11yescharacteristic
446C2×C4C11×2−1+411yescharacteristic
447C8—22no—
448C8—22no—
449C8—42no—
450C22—24no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—42no—
455C22—42no—
456C22—42no—
457C22C2×C4×D4×C1111yescharacteristic
458C22C11×#54611yescharacteristic
459C22C11×#54811yescharacteristic
460C22C22×C11×SD1611yescharacteristic
461C22C2×C11×#13511yescharacteristic
462C22C11×#57611yescharacteristic
463C22C11×#57811yescharacteristic
464C4—22no—
465C4—24no—
466C4—42no—
467C4—42no—
468C4—42no—
469C4—42no—
470C4—82no—
471C4—82no—
472C4C4×C11×SD1614yes—
473C4C2×C11×#11711yescharacteristic
474C4C11×#52011yescharacteristic
475C4C11×#55211yescharacteristic
476C4C11×#55311yescharacteristic
477C2—44no—
478C2C11×#235211yescharacteristic
479C2C2×C4×C11×SD1611yescharacteristic
480C2C11×#295111yescharacteristic
481C2C11×#329511yescharacteristic
482C2C11×#330211yescharacteristic
483C2C11×#335911yescharacteristic
484C2C11×#336111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C11×#2355C2semidirect
4. C11×#1933C2semidirect
5. C11×#1919C2semidirect
7. C11×#1834C2semidirect
8. C11×#1803C2semidirect
10. C8×C11×C4⋊C4C2semidirect
17. C4×C11×SD16C4semidirect
53. C4×Q8×C11C2×C4semidirect
77. C11×#106C2×C4semidirect
80. C11×#103C2×C4semidirect
84. C4×C8×C11C2×C4semidirect
90. #22770C11direct (N × H)
143. C11×C4⋊C4SD16semidirect
155. #2355C2×C11semidirect
157. #1933C2×C11semidirect
158. #1919C2×C11semidirect
160. #1834C2×C11semidirect
161. #1803C2×C11semidirect
163. C8×C4⋊C4C2×C11semidirect
224. C4×SD16C4×C11semidirect
287. C4×Q8C2×C4×C11semidirect
311. #106C2×C4×C11semidirect
314. #103C2×C4×C11semidirect
318. C4×C8C2×C4×C11semidirect
384. C4⋊C4C11×SD16semidirect
395. C11#22770direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C4×C11×SD162
C11×#23552
D4×C11×C4⋊C42
C11×#19332
C11×#19192
C11×#18772
C11×#18342
C11×#18032
C11×#18022
C8×C11×C4⋊C42
C4×C11×#1022
#2277011